{"id":"openai-math/GOE-bulk-universality-for-fixed-degree-random-regular-graphs","pdf":"https://github.com/openai/math/blob/main/preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/GOE-bulk-universality-for-fixed-degree-random-regular-graphs-September-23-2026","tags":["random-matrices","random-graphs","spectral-theory"],"score":0,"title":"GOE bulk universality for fixed-degree random regular graphs","domain":"Probability and statistical mechanics","family":"219","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove the fixed-degree bulk-universality conjecture for random regular graphs. For every fixed integer d ≥ 3 and every fixed energy in the open Kesten–McKay bulk, the unfolded eigenvalue point process of the adjacency matrix of a uniform simple labelled d -regular graph converges to the GOE bulk process. The convergence holds along all admissible graph sizes, without additional conditioning.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"GOE bulk universality for regular graphs with weak Anderson disorder"}